Suppose a single die is rolled, Find:
a)P(6, given that an odd number was rolled)
b) P(5, given that an odd number was rolled)
To find the probabilities, we need to determine the number of favorable outcomes and the number of total outcomes.
Since a single die is rolled, there are 6 possible outcomes: {1, 2, 3, 4, 5, 6}.
a) P(6, given that an odd number was rolled):
Out of the 6 possible outcomes, there are three odd numbers: {1, 3, 5}.
Since an odd number is rolled, we consider the favorable outcomes to be {1, 3, 5}.
Therefore, the probability of rolling a 6, given that an odd number was rolled is 0, as there are no favorable outcomes for rolling a 6 when an odd number is rolled.
Therefore, P(6, given that an odd number was rolled) = 0.
b) P(5, given that an odd number was rolled):
Similar to the previous case, there are three odd numbers: {1, 3, 5}.
Since an odd number is rolled, we consider the favorable outcomes to be {1, 3, 5}.
Among these favorable outcomes, there is one 5.
Therefore, the probability of rolling a 5, given that an odd number was rolled is 1/3.
Therefore, P(5, given that an odd number was rolled) = 1/3.
To find the probability of rolling a specific outcome given a specific condition, we need to consider the total number of favorable outcomes and the total number of possible outcomes.
Let's calculate the probabilities for both cases:
a) P(6, given that an odd number was rolled)
To find the probability of rolling a 6 given that an odd number was rolled, we first need to determine the total number of favorable outcomes and the total number of possible outcomes.
Total number of favorable outcomes:
Since an odd number was rolled, the only favorable outcome is rolling a 6, which occurs 1 time.
Total number of possible outcomes:
When rolling a die, the total number of possible outcomes is 6 since there are 6 sides on a die.
Therefore, the probability of rolling a 6 given that an odd number was rolled is:
P(6, given that an odd number was rolled) = Favorable outcomes / Total outcomes
P(6, given that an odd number was rolled) = 1 / 6
b) P(5, given that an odd number was rolled)
Similarly, let's calculate the probability of rolling a 5 given that an odd number was rolled.
Total number of favorable outcomes:
Since an odd number was rolled, the only favorable outcome is rolling a 5, which occurs 1 time.
Total number of possible outcomes:
When rolling a die, the total number of possible outcomes is 6 since there are 6 sides on a die.
Therefore, the probability of rolling a 5 given that an odd number was rolled is:
P(5, given that an odd number was rolled) = Favorable outcomes / Total outcomes
P(5, given that an odd number was rolled) = 1 / 6
So, both probabilities are the same: P(6, given that an odd number was rolled) = P(5, given that an odd number was rolled) = 1 / 6.
a) If you an odd number with a single die, how can the total be 6?
b) There are three possible odd-number tosses. One of them is 5.
Try to think these through on your own